Step 1: | Decide if the four terms have anything in common, called the greatest common factor or GCF. If so, factor out the GCF. Do not forget to include the GCF as part of your final answer. |
Step 2: | Every difference of squares problem can be factored as follows: a^{2} – b^{2} = (a + b)(a – b) or (a – b)(a + b). So, all you need to do to factor these types of problems is to determine what numbers squares will produce the desired results. |
Step 3: | Determine if the remaining factors can be factored any further. |
Example 1 – Factor:
Step 1: Decide if the four terms have anything in common, called the greatest common factor or GCF. If so, factor out the GCF. Do not forget to include the GCF as part of your final answer. In this case, the two terms only have a 1 in common which is of no help. | |
Step 2: To factor this problem into the form (a + b)(a – b), you need to determine what squares will equal x^{2} and what squared will equal 36. In this case the choices are x and 6 because (x)(x) = x^{2} and (6)(6) = 36. | |
Step 3: Determine if any of the remaining factors can be factored further. In this case they can not so the final answer is: |
Example 2 – Factor:
Step 1: Decide if the four terms have anything in common, called the greatest common factor or GCF. If so, factor out the GCF. Do not forget to include the GCF as part of your final answer. In this case, the two terms only have a 1 in common which is of no help. | |
Step 2: To factor this problem into the form (a + b)(a – b), you need to determine what squares will equal 4x^{2} and what squared will equal 81. In this case the choices are 2x and 9 because (2x)(2x) = 4x^{2} and (9)(9) = 81. | |
Step 3: Determine if any of the remaining factors can be factored further. In this case they can not so the final answer is: |
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Example 3 – Factor:
Step 1:Decide if the four terms have anything in common, called the greatest common factor or GCF. If so, factor out the GCF. Do not forget to include the GCF as part of your final answer. In this case, the two terms have a 2 in common, which leaves: | |
Step 2: To factor this problem into the form (a + b)(a – b), you need to determine what squares will equal 9x^{2} and what squared will equal 49y^{2}. In this case the choices are 3x and 7y because (3x)(3x) = 9x^{2} and (7y)(7y) = 49y^{2}. | |
Step 3: Determine if any of the remaining factors can be factored further. In this case they can not so the final answer is: |
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Example 4 – Factor:
Step 1:Decide if the four terms have anything in common, called the greatest common factor or GCF. If so, factor out the GCF. Do not forget to include the GCF as part of your final answer. In this case, the two terms have a 9x in common, which leaves: | |
Step 2: To factor this problem into the form (a + b)(a – b), you need to determine what squares will equal x^{2} and what squared will equal 9. In this case the choices are x and 3 because (x)(x) = x^{2} and (3)(3) = 9. | |
Step 3: Determine if any of the remaining factors can be factored further. In this case they can not so the final answer is: |
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Example 5 – Factor:
Step 1: Decide if the four terms have anything in common, called the greatest common factor or GCF. If so, factor out the GCF. Do not forget to include the GCF as part of your final answer. In this case, the two terms only have a 1 in common which is of no help. | |
Step 2: To factor this problem into the form (a + b)(a – b), you need to determine what squares will equal 16x4 and what squared will equal 1. In this case the choices are 4x^{2} and 1 because (4x^{2})(4x^{2}) = 16x^{4} and (1)(1) = 1. | |
Step 3: Determine if any of the remaining factors can be factored further. In this case one of the factors is a difference of squares, which factors and the other factor is a sum of squares which does not factor. To factor the difference of squares, you need to determine what squares will equal 4x^{2} and what squared will equal 1. In this case the choices are 2x and 1 because (2x)(2x) = 4x^{2} and (1)(1) = 1. So, the final answer is: | |
Step 4: Determine if any of the remaining factors can be factored further. In this case they can not so the final answer is: |